What would you have to invest today at 5% interest compounded monthly if you wish to have $20,000 in 10 years?

Question

parthkohli · Answer

$$P\left(1 + \dfrac{5}{12\cdot 100}\right)^{10 \cdot 12} = 20000$$Solve for $P$

anonymous · Answer

What should i do if my calulater keeps saying ERR: Overflow

parthkohli · Answer

OK, let me explain. You must divide both sides by $\left(1 + \dfrac{5}{12 \cdot 100}\right)^{10 \cdot 12}$.

parthkohli · Answer

$$P\left(1 + \dfrac{1}{240}\right)^{120} = 20000$$

anonymous · Answer

Order of operations.

parthkohli · Answer

OK wait, is that 5% per month or per annum?

parthkohli · Answer

Wait a second.

parthkohli · Answer

$$P\left(1 + \dfrac{5}{100}\right)^{120} = 20000$$If that is 5% per month, then it is a little easier...

anonymous · Answer

and where did you get 100 from should it no be 10 because when i look back at the book she claims that you would do 12 for the number of months in a year and there are 10 years

parthkohli · Answer

The formula for compound interest is,$$P \left(1 + \dfrac{r}{100}\right)^n$$

parthkohli · Answer

$n$ is the number of times it is compounded, which would be $12 \times 10 = 120$ and $r$ is the rate which is $5$. But does the amount compound monthly or yearly?

anonymous · Answer

monthly and my book say r over n not 100

parthkohli · Answer

Hmm, don't get confused with that. Our books mean different stuff. Your book means $r\%$ by $r$.

parthkohli · Answer

Oh, I meant to ask if it was 5% annually or monthly.

parthkohli · Answer

I'd assume that it means annually.$$P\left(1 + \dfrac{5}{100 \cdot 12}\right)^{12 \times 10} = 20,000$$

anonymous · Answer

its monthly and the is my formula 

A=P(1+ R/N) raise NT    (sorry i cant do the upsidedown V)